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193
1. .
,
.
xOy,
( ).
:
.
2. .
,
0 ,
.
,
,
.
:
y
x
y
G
yG
0G
gG
0G
BG
h
O
x
194
.
, :
,
t,
,
t .
:
(xx): x = 0 = .
x = 0 t
(yy):
2
u g t1
y g t2
= =
H
x = 0 y = g t .
:
( )= + = + 22 2 2x y 0 g t 0 :
= =yx 0
g t
27 ( ) 0 h
t = 0 . N
:
. .
. ,
.
. ,
().
. ,
.
195
. .
: h, o, g.
A
0G
dh
x , :
xx: x = 0 (1) x = 0 t (2) yy: y = g t (3) y = g t2 (4) . (2) (4) .
:
(2) 0
xt
= (5)
(4) 2 2(5)
20 0
1 x 1 xy g y g
2 2 = = =
220
gy x
2(6)
. : (4)
2
1y h h gt
2= = = 2ht g (7)
. At t x x= = , :
(2), (7) = 0 2hx g (8)
196
. d
:
2 2 2 2 2A Ad h x d h x = + = + = +
22 02hd h
g (9)
. y Ayt t = =
(3), (7) Ay Ay2h
g 2ghg
= = (10)
: (10)
2 2A A Ay (1)
(10)Ay
(1)A
= + = +
= =
2A 0
0
2gh
2gh
28 h = 320 m, 0 100m/s,
=30 m/s.
:
i) .
ii) .
i) .
, , 0 h.
. :
xx: x = 0 (1) x = 0 t (2)
yy: y = g t (3) y = t2 (4)
(4) . :
(4)2
1 2h 2 320y h h gt t 64
2 g 10= = = = = t = 8 s
x1:
(2) => x1 = 0 t x1 = 1008 x1 = 800 m
197
,
x2 :
x2 = t x2 = 308 x2 = 240 m
H d, :
d = x1 - x2 d = 800 - 240 d = 560 m ii) .
. d ( ) :
d = x1 + x2 d = 800 + 240 d = 1040 m
G
d x2
0G
d h
x1
198
29 , 7,2 m
3 s.
.
;
.
12 m/s ,
i)
;
ii) ;
A. , :
h = g t2 => g = 2t2h
=> g = 1,6 m/s2
B.
:
xx: x = 0 = . (1) x = 0 t (2) yy: y = g t (3) y = g t2 (4)
i) y = h )4(h = g t2 =>
g2h t = => t = 3 s
ii) (2) => x = 123 => x = 36 m
h
0G
199
3. .
xG
,
.
xG
.
.
t1 t2,
. .
:
,
G
3
G
2
G
1
O
y
x
xG
xG
2
xG
1
O
y
x
200
, .
R
2
= ,
.
, ,
, .
.
:
Fk = m k Fk = m 2
R
4. .
,
.
(...).
.
:
GG
G
G
201
(): ,
.
t :
t =
1 s (1 ).
(f): .
t : = Nft
SI = =11 s 1 zs
(1 Herz).
: 1 kz = 103 Hz, 1 MHz = 106 Hz, 1 GHz = 109 Hz.
N
ft
= , ( = 1)
(t = T), : = 1fT
.
(G ): , ,
S .
,
,
:
= S t
: S=2R
t = T, :
= =2 R 2 R f T
S.I. 1 m/s.
G
S
G
G
G
202
(G ): , ,
.
,
,
t :
t =
: = 2 t = T,
:
= =2 2 f T
SI 1 rad/s (
),
rad () ().
: =180
180 .
:
R K K 2
2R
K
u 2 R f
u R
2 f
F F m au
F mu RaR
= = = = = = = = = =
= = = =
S 2 R
t TN 1ft T
2 t T
1f
T
G
G
G
203
. .
: 1
: . gm GG =
: .
:
, . KFT = : .
2 . ,
(xOx),
.,
(yOy)
.
3 . .
.
ru
mamF2
K)
(r == , ( ).
4
amFx = ,
. ,
.
5 , .
204
30 ( ) , R = 20 cm 10
t = 2 s. :
. .
. .
. . 2 = 10.
. M . :
==210
tN
f f = 5 Hz
:
= Rf 2 = 2 m/s . :
==RR = 10 rad/s
. :
=R
2
k = 200 m/s2
,
,
:
= 0
31 ( ) .
T1 = 2 s T2 = 3 s. t =
0 .
. :
i) .
205
ii) .
. .
.
i) 1, 2
().
, :
1 2 1 2 1 21 2
2 2 2 t t 2 ( )t 2 t 2
/ / = = = = /
2 1 1 2
1 2 1 2 2 1
1 1t 1 t 1 t
= = =
t = 6 s
ii) 1, 2
().
, :
1 2 1 2 1 21 2
2 2 2 t t 2 ( )t 2 t 2
/ /+ = + = + = + = /
1 2 1 2
1 2 1 2 1 2
1 1t 1 t 1 t
+ + = = = +
t = 1,2 s
. ,
, ,
.
1 :
1
t t 2,4,6,8,10,12,...= = (1) 2 :
2
t t 3,6,9,12,15,...= = (2)
1, 2.
(1), (2) t 6,12,18,... = ... 1, 2. t = 6 s.
206
32 ( ) A = 1 m
. .
o60 = , = 2 m/s. ,
. m = 10 kg, g = 10 m/s2.
:
:
+==== AAA222
2
R
m mg T m mg - T m R
m F
= 90
Fy = m y = m mg= m = g = 10 23
= 5 3 m/s2
207
33 ( ) m = 1000 kg R = 100 m,
.
; = 0,4 g =
10 m/s2.
:
( ) ,
.
.
=
=====
==
mgN
mgBN0 B - N0FR
mR
mF
y
22
R
==/=/ gRgRRm
gm 22
= 20 m/s
= 20 m/s,
= mg. .
NG
BG
TG
208
.
1. m R, ,
:
. .
. .
. m2/R.
. .
;
2.
, :
. .
. .
. .
. .
. .
3. m = 4 kg, r = 1 m.
100 , :
. .
. .
. .
. .
4. ,
A , : . ,
.
. .
. TG
, .
.
209
.
;
5. :
. .
. .
. ,
().
.
.
x .
6.
( )
;
x .
7.
;
. .
. .
. .
. .
8. .
, :
210
.
.
. .
. .
. .
( )
9. :
. .
. .
. .
. .
. m/r.
. .
. .
. .
;
10. Luna-Park
. ,
, mg, :
. mg . 2mg . 3mg . 4mg
11. .
. ,
:
. 3/2 . 3/4 . 9/4 . 1/2
211
12. 1m, 2 kg. ,
.
4m/s, (g=10m/s2):
. 0 . 20 . 32 . 52
13. 50 m,
. 0,8.
( km/h)
; g=10m/s2:
. 108 . 36 . 72 . 90
14. 1000 kg, 10 m/s
( ) 100 m.
250 . ;
. .
. .
. .
.
212
. 1. h = 320 m 0 =
60 m/s. :
. .
. .
. .
. .
g = 10 m/s2.
(. 8 s 480 m 100 m/s = 4/3 577 m)
2. 0 = 10 m/s,
t = 1 s:
. .
. .
g = 10 m/s2.
(. 10 2 m/s = 45 10m 5m)
3. 0 = 100 m/s. :
.
.
.
.
g = 10 m/s2.
(. 20 s 40 2 s)
4. 0 = 10 m/s h = 80 m.
. 0 2
x 2 ,
x ;
g = 10 m/s2.
(. 40 m 1 s 2 s)
213
5. h = 20 m 01 = 100 m/s.
d ,
02 = 20 m/s. :
. d
. .
g = 10 m/s2.
(A. 100 m 15 m)
6.
= 30, x1 = 1,6 m.
x2 = 1 m, ,
x3 = 0,5 m.
.
: h = 1,25 m, g = 10 m/s2.
(. 0,75)
. 7. m = 200 g A = 1,5 m,
.
1 min 120 . 2 10: . .
. .
. .
. .
. g = 10 m/s2.
(. 6 m/s 0,5 s 4 rad/s 48 2 )
8. R = 10 m.
= 0,4 rad/s. :
h
x3
x2
x1
30
214
. .
. t = 2 min.
(. 0,2 Hz 5 s 24)
9. = 120. R = 50 m.
100/3 s, :
. .
. .
(. 0,02 rad/s m/s 0,01Hz 100s)
10. R = 2 m.
t = 4 s
. :
. .
. .
(. 0,125 Hz 8 s /4 rad/s /2 m/s)
11. m = 2 kg R = 1 m.
t = 5 s 20 . :
. .
. .
. . (2 = 10).
(. 4 Hz 0,25 s 8 m/s 8 rad/s 640 m/s2 1280 N)
12. m = 0,1 kg R = 0,5 m
. t = 10 s 600 .
(2=10).
(. 7200 N)
13. m = 2 kg R = 1 m.
0,8
m.
g = 10 m/s2 2 = 10.
(. 500)
215
14. ** N .
12 .
/3 ;
(. 12 h 1 h 10,9 min)
.
15. R = 120 3 m.
216 Km/h,
. g = 10 m/s2.
(. 30)
16. R = 90 m = 10 m/s.
;
g = 10 m/s2.
(. = 9)
17. m = 1200 kg,
= 54 km/h. R = 60 m.
,
.
g = 10 m/s2.
(. 4500 0,375)
18. 310R = m, 30 .
.
, .
g = 10 m/s2.
(A. 10 m/s)
19. Luna Park
, .
- 50 kg.
216
R
R = 10 3 m = 30,
.
g = 10 m/s2.
(. 1000 1 rad/s)
20. m = 0,2 kg A = 0,5 m.
R = 0,3 m
(
). g = 10 m/s2, :
. .
. .
. .
. = 60.
(. 1,5 m/s 2,5 N 5/2 z /15 s)
21. m = 1 kg , A = 0,8 m = 80 .
f ;
(A. 5/ Hz)
22. 70 kg "" Luna Park.
"" R = 10 m = 1
m/s,
.
g = 10 m/s2.
(A. 693 707 )
23.
( ), R = 12,5 m,
; -
= 0,8 g = 10 m/s2.
(. 1/2 z)
A
m K R
G
217
24.
. 20 cm
,
50 .
.
g = 10 m/s2 2 = 10.
(. 5/9)
25. 5000 Kg 36
Km/h, . 2
. ( ),
50 m ( ).
45000 N. ;
.
26. R = 1,6 m.
, ;,
g = 10 m/s2.
(. 4 m/s)
218
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